A Syrian woman carries her child from a tent fire at Zattari refugee camp on the Syria-Jordan border. Photograph: Chen Chunxiang/Corbis

The number of refugees from the Syrian conflict, which topped 1 million last week, could triple by the end of the year if it continues at the current rate, the UN’s refugee chief said on Sunday.

“If this escalation goes on, we will have – and nothing happens to solve the problem – we might have in the end of the year a much larger number of refugees, two or three times the present level,” the UN high commissioner for refugees, António Guterres, told reporters in Ankara.

If his worst forecast comes true, it would make Syria the world’s biggest refugee problem area, ahead of Afghanistan and Iraq.

Thousands of refugees are crossing into Jordan, Turkey and Lebanon every day. Half are children.

Lebanon’s population has increased by 10% as a result of the refugee inflow, the UN refugee agency reported last week. Tens of thousands of refugees have even crossed into Iraq, despite the uncertain security situation there.

Map – Syrian refugee numbers Aid agencies have warned that they are receiving insufficient funds to deal with the huge numbers flowing into camps such as Zaatari on the Syria-Jordan border.